Private costs + External costs = Social costs
The private costs are those costs that are paid for by someone who produces or consumes a good or service.
For example, the driver of a car pays for the insurance, road tax, petrol and the cost of purchasing the car.
The external costs are the negative side-effects of production or consumption incurred by third parties, for which no compensation is paid.
For example, a car driver does not pay for the cost of the congestion and air pollution created when driving the car.
The social costs are the total costs to society.
The true cost of a car journey is called the social cost.
There is a market failure because the private costs (of driving) do not represent the true costs (of driving) to society.